If you don't want to get involved in soldering then buy a relay shield with screw terminals and have that turn a compressor on for a pre-set period of time.
I am sure the compressor would easily generate enough pressure, but it would probably be very slow. You may also have problems with the air leaking back out when the compressor is off. I suspect they usually rely on the fact that car tyres have built-in non-return valves.
But hey - just try it, the relay shield will probably be part of the answer whatever eventually works.
Si.